This invention relates to a reactor power measuring method. More particularly, it relates to a reactor power measuring method for measuring the power distribution in the core of a nuclear reactor by the use of neutron detectors.
An in-core power profile of a nuclear reactor provides information important for operating the nuclear reactor, and several methods for measuring it have heretofore been tried. One of them is a method wherein a large number of stationary-type small-sized neutron detectors are installed in the nuclear reactor. With this method, replacement of a detector due to a malfunction thereof is difficult, and hence, the detector is required to operate properly for a long term. However, it has been very difficult to fabricate such a detector. The second method is a method wherein small-sized neutron detectors are successively inserted into a large number of detector insertion holes provided in the nuclear reactor, thereby to measure the reactor power profile while the nuclear reactor is being scanned. This method has the disadvantage that a long time is required for measuring the reactor power profile over the whole nuclear reactor and, accordingly, that reactor power profiles which change in a short time cannot be followed. The third method is a method wherein the detectors of a neutron measurement device are installed outside the reactor. This device has hitherto been used for measuring the reactor power of a pressurized water reactor (PWR) and is divided in the axial directions thereof into a large number of shorter detectors, the output signals of which are utilized to calculate the reactor power profile.
The third method mentioned above will now be explained with reference to FIG. 2. In the figure, numeral 100 designates the core of the PWR, which is divided into parts 101-104 in the axial direction thereof. Numerals 210, 220, 230 and 240 indicate neutron detectors, respectively. Numerals 211-214, 221-224, 231-234 and 241-244 indicate divided partial detectors of the neutron detectors 210, 220, 230 and 240, respectively.
Though not shown, the scanning type neutron detectors within the core as explained in connection with the second method mentioned above are disposed in the reactor core, so that the in-core power profile f(x, y, z) of the nuclear reactor is obtained. The device illustrated in FIG. 2 serves to find the mean value f(z) (the power profile in the vertical direction) of the reactor power profile f(x, y, z) for given xy-planes (horizontal planes). ##EQU1## (S.sub.xy : horizontal sectional area of the core) Here, f(z) can be expressed as the summation of a Fourier series by the following: ##EQU2## (where Z.sub.max : height of the core)
In this regard, since the reactor power profile decreases at the upper and lower ends of the core, the equation is expressed by a sine series having a domain of 0-.pi.. The coefficient C.sub.i is evaluated from the axial power profile f(z), and an equation for evaluating C.sub.i from f(z) is the so-called Fourier series expansion, which is given by the following equation: ##EQU3## Here, in this device, the above coefficient needs to be determined from the output signal values of the partial detectors 211-214, etc. It is therefore convenient to use the following equation instead of Eq. (3): EQU [C.sub.i ]=[A.sub.ij ][f.sub.j ] (4)
where ##EQU4## [A.sub.ij ] denotes a constant coefficient matrix, which is obtained by solving Eq. (2) integrated over the respective sections i. The quantity f.sub.j is obtained in such a way that f(z) is integrated in the direction of a Z-axis for the respective reactor parts 101-104. It has the relation of the following equation to the outputs of the partial detectors 211-214, etc. EQU [D.sub.k ]=[Q.sub.kj ][f.sub.j ] (5)
Here, D.sub.k is defined to be D.sub.1 for the mean value of the outputs of the partial detectors 211, 221, 231 and 241; to be D.sub.2 for the mean value of the outputs of the partial detectors 212, 222, 232 and 242; and so on. [Q.sub.kj ] denotes a constant coefficient matrix whose coefficients are the rates of contribution of the powers of the respective parts of the core to the corresponding partial detectors.
From Eqs. (4) and (5), the Fourier coefficient C.sub.i is obtained as follows. EQU [c.sub.i ]=[A.sub.ij ][Q.sub.kj ].sup.-1 [D.sub.k ] (6)
Further, the power profile f(z) in the axial direction of the core is evaluated in accordance with Eq. (2).
With the reactor power measuring method of the prior art as thus far described, for the purpose of determining the constant coefficient maxtrix [Q.sub.kj ] of Eq. (5), a plurality of sets of the detector outputs [D.sub.k ] and the integral values f.sub.j of the powers of the reactor parts need to be prepared for determining different reactor power profiles. The number of the sets must be, at least, the number of divisions (four in FIG. 2) of the partial detectors. Another problem is that, unless the reactor power profiles of the respective sets are sufficiently different, the calculation of the matrix [Q.sub.kj ] becomes difficult.